Range of Y question

Hello, I wonder if anyone can help me, would be very grateful if anyone could.

If you wanted to find the range of a curve say y=(2x^2
+ 5x+3)/(4x^2 + 5x +3) instead of using calculus to find the stationary points and then subing back in to find e.g. the min. value of y or whatever, you can rearrange :